Asymptotic behavior of energy band associated with a negative energy level

The mathematical foundation of the tight binding approximation is given. If ₀ is a negative energy level of a real potentialq, then there exists an energy band for a one-dimensional chain with period 2T of the same atoms which lies near ₀. We study this band whenT tends to infinity.On leave of absence from the Department of Physics, Leningrad State University, Leningrad, USSR.     

On concepts of directional differentiability

Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of Gâteaux, Fréchet, and Hadamard are singled out from the general framework of -directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equivalent. The chain rule for directional derivatives of a composite mapping is discussed.     

Random walks generated by affine mappings

This article is concerned with Markov chains on ^m constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic.     

新的酰胺型开链冠醚的合成与性质

Simon在70年代开发了一类酰胺型开链冠醚,能选择性配位碱土金属离子并可作为中性载体制备离子选择性电极.由于酰胺型开链冠醚易于制备,因此受到人们广泛地重视.Vgtle等提出的“末端基”概念为开链冠醚的合成、设计起了重要的指导作用.前文报道2-甲氧基-1-氨甲基萘与三甘醇二碘化物在无水碳酸钠存在下于乙腈中反应得到双手臂的套索冠醚与碘化钠的配合物.X射线衍射晶体结构分析表明萘环上的甲氧基中的氧原子参加了与钠离子的配位,生成了扭曲的六边形双锥结构配合物.因此2-甲氧基-1-氨基萘可以作为开链冠醚的“末端基”.开链冠醚的合成路线是:     

MONTE CARLO STUDY ON THE CRITICAL ADSORPTION POINT OF BOND-FLUCTUATED POLYMER CHAINS TETHERED ON ADSORBING SURFACES

 The behavior of three-dimensional bond fluctuation model chains tethered on an adsorbing flat surface was simulated by the Monte Carlo method. The dependence of the number of surface contacts M on the interaction strength e and the chain length N was investigated by a finite-size scaling law M = N[a₀ + a₁N^1/v_k + O((N ^1/v_k)²)] for e near the critical adsorption point e_c, i.e., k ≡(e-e_c)/e_c closes to 0. The critical adsorption point was estimated to be e_c = 0.93, and the exponents  = 0.49 and 1/v= 0.57.     

Stereoselective electrocatalytic cyclization of 3-substituted 2,2-dicyanocyclopropane-1,1-dicarboxylic acid esters to form 6-substituted (1R,5R,6R)*-4,4-dialkoxy-5-cyano-2-oxo-3-azabicyclo[3.1.0]hexane-1-carboxylic acid esters

Electrolysis of 3-substituted 2,2-dicyanocyclopropane-1,1-dicarboxylic acid esters in alcohols in an undivided cell in the presence of NaBr or NaOAc afforded 6-substituted (1R,5R, 6R)*-4,4-dialkoxy-5-cyano-2-oxo-3-azabicyclo[3.1.0]hexane-1-carboxylic acid esters in 80–95% yields. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 102–107, January, 2006.     

Detection of processed genetically modified food using CIM monolithic columns for DNA isolation

The availability of sufficient quantities of DNA of adequate quality is crucial in polymerase chain reaction (PCR)-based methods for genetically modified food detection. In this work, the suitability of anion-exchange CIM (Convective Interaction Media; BIA Separations, Ljubljana, Slovenia) monolithic columns for isolation of DNA from food was studied. Maize and its derivates corn meal and thermally pretreated corn meal were chosen as model food. Two commercially available CIM disk columns were tested: DEAE (diethylaminoethyl) and QA (quaternary amine). Preliminary separations were performed with standard solution of salmon DNA at different pH values and different NaCl concentrations in mobile phase. DEAE groups and pH 8 were chosen for further isolations of DNA from a complex matrix-food extract. The quality and quantity of isolated DNA were tested on agarose gel electrophoresis, with UV-scanning spectrophotometry, and by amplification with real-time PCR. DNA isolated in this way was of suitable quality for further PCR analyses. The described method is also applicable for DNA isolation from processed foods with decreased DNA content. Furthermore, it is more effective and less time-consuming in comparison with the existing proposed methods for isolation of DNA from plant-derived foods.     

Synthesis and Structure of a Manganese(Ⅱ) Complex: [Mn2·(dinitrobenzoic acid)4·(1,10-phen)2]n

The title compound, [Mn2·(dinitrobenzoic acid)4·(1,10-phen)2]n, has a linear chain structure containing binuclear [Mn2·(dinitrobenzoic acid)4(1,10-phen)2] repeat units. It crystallizes in the triclinic system, space group P1- with a = 7.9261(8), b = 12.1329(15), c = 14.847(2)(A), α = 103.845(5), β =101.424(5), γ= 92.618(4)°, Mr= 657.37, V= 1352.3(2) (A)3, Z = 2, Dc= 1.614 g/cm3, F(000) = 666, μ =0.567 mm-1, the final R = 0.0407 and wR = 0.1015 for 4081 observed reflections with I ＞ 2σ(Ⅰ). The Mn atom is six-coordinated by two N and four O atoms, forming a slightly distorted octahedral geometry. All Mn-O and Mn-N bond distances range from 2.093(2) to 2.310(2)(A). Two adjacent octahedral units are bridged together by two pairs of bi-monodentate carboxyl groups of different dinitrobenzoic acids to form an eight-membered ring with chair-typed configuration, thus generating a one-dimensional chain along the a axis.     

Synthesis, Crystal Structure and Electrochemical Properties of One-dimensional Chain Coordination Polymer [Co(Ⅱ)(C6H5CH=CHCOOH)2(4,4''-bipy)(H2O)5]n

A one-dimensional chain coordination polymer [Co(Ⅱ)(C6H5CH=CHCOOH)2(4,4'-bipy)(H2O)5]n has been synthesized with cinnamylic acid, 4,4'-bipy and cobaltous chloride as raw materials. Crystal data for this complex: monoclinic, space group P21/c, a - 1.1481(3), b =1.1230(2), c = 1.1759(3) nm, β = 97.054(4)°, V = 1.5046(6) nm3, Mr= 617.50, Dc = 1.363 g/cm3, Z= 2, μ(MoKα) = 0.627 mm-1, F(000) = 646, S = 1.062, R 0.0443 and wR = 0.1178. The crystal structure shows that two neighboring cobalt(Ⅱ) ions are linked together by one 4,4'-bipy, and the whole complex molecule adopts a one-dimensional chain structure. Each cobalt(Ⅱ) ion is coordinated with two nitrogen atoms from two 4,4'-bipy molecules and four oxygen atoms from four water molecules, giving a distorted octahedral coordination geometry. The electrochemical properties were analyzed by combining with the crystal structure.